SYSC 2510
Probability, Statistics and Random Processes for Engineers
Discrete and continuous random variables. Joint and conditional probabilities, independence, sums of random variables. Expectation, moments, laws of large numbers. Introduction to statistics. Stochastic processes, stationarity, additive white Gaussian noise, Poisson processes. Markov processes, transition probabilities and rates, birth death processes, introduction to queueing theory.
2020
Topics
- Random experiment, statistical regularity, relative frequency, sample space.
- Set theory, axioms of probability, computing probabilities using counting
- methods.
- Conditional probability, independence of events, sequential experiments.
- Discrete and continuous random variables, probability mass function.
- Cumulative distribution function (cdf), probability density function (pdf)
- conditional cdf’s and pdf’s, expected value.
- Some important continuous random variables, functions of a random variable
- Markov and Chebyshev inequalities.
- Transform methods, computer generation of random variables, pairs of random
- variables.
- expectation, vector random variables.
- Functions of several random variables, expected values of vector random
- variables, Jointly Gaussian random vectors.
- Random processes; mean, autocorrelation, and auto-covariance functions
- stationary random processes.
- Power spectral density, Markov processes, introduction to queueing theory.
Prerequisites & course information
Prerequisite(s): MATH 1004 and MATH 1104 . Lectures three hours a week, laboratory three hours alternate weeks.